Let be a function such that . Show that for any continuous function ,we ahve the sequence converges uniformly on the compact sets of to f(x)

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- Jul 10th 2012, 10:18 PMproblemUniform Convergence
Let be a function such that . Show that for any continuous function ,we ahve the sequence converges uniformly on the compact sets of to f(x)

- Jul 11th 2012, 12:57 AMgirdavRe: Uniform Convergence
First, use the substitution in the integral (the integration is with respect to ). I think we have to assume bounded, because if is not integrable (for example when , and , we have some problems.